CHAPTER 13
CHAPTER 13
IMPERFECT COMPETITION:
A GAME-THEORETIC APPROACH
McGraw-Hill/Irwin
Copyright © 2006 The McGraw-Hill Companies, Inc. All rights reserved.
Chapter Outline
AN INTRODUCTION TO THE THEORY OF GAMES
SOME SPECIFIC OLIGOPOLY MODELS
COMPETITION WHEN THERE ARE INCREASING
RETURNS TO SCALE
MONOPOLISTIC COMPETITION
A SPATIAL INTERPRETATION OF
MONOPOLISTIC COMPETITION
HISTORICAL NOTE: HOTELLING’S HOT DOG
VENDORS
CONSUMER PREFERENCES AND ADVERTISING
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Prisoner's Dilemma
Two prisoners are held in separate cells for a
serious crime that they did in fact commit. The
prosecutor has only enough hard evidence to
convict them of a minor offense, for which the
penalty is a year in jail. Each prisoner is told that
if one confesses while the other remains silent, the
confessor will go scot-free while the other spends
20 years in prison. If both confess, they will get an
intermediate sentence 5 years.
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Dominant Strategy
Dominant strategy: the strategy in a game
that produces better results irrespective of
the strategy chosen by one’s opponent.
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The Nash Equilibrium Concept
Nash equilibrium: the combination of
strategies in a game such that neither player
has any incentive to change strategies given
the strategy of his opponent.
A Nash equilibrium does not require both
players to have a dominant strategy!
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The Maximin Strategy
Maximin strategy: choosing the option that
makes the lowest payoff one can receive as
large as possible.
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Tit-for-Tat
Tit-for-tat strategy: The first time you interact
with someone, you cooperate. In each subsequent
interaction you simply do what that person did in
the previous interaction. Thus, if your partner
defected on your first interaction, you would then
defect on your next interaction with her. If she
then cooperates, your move next time will be to
cooperate as well.
Requirement: there not be a known, fixed number of
future interactions.
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Sequential Games
Sequential game: one player moves first, and the
other is then able to choose his strategy with full
knowledge of the first player’s choice.
Example - United States and the former Soviet Union
(USSR) during much of the cold war.
Strategic entry deterrence – they change potential
rivals’ expectations about how the firm will
respond when its market position is threatened.
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Figure 13.1: Nuclear Deterrence
as a Sequential Game
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Figure 13.2: The Decision to Build
the Tallest Building
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Figure 13.3: Strategic Entry
Deterrence
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The Cournot Model
Cournot model: oligopoly model in which
each firm assumes that rivals will continue
producing their current output levels.
Main assumption - each duopolist treats the
other’s quantity as a fixed number, one that will
not respond to its own production decisions.
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Figure 13.4: The Profit-Maximizing
Cournot Duopolist
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The Cournot Model
Reaction function: a curve that tells the
profit-maximizing level of output for one
oligopolist for each amount supplied by
another.
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Figure 13.5: Reaction Functions
for the Cournot Duopolists
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The Bertrand Model
Bertrand model: oligopoly model in which
each firm assumes that rivals will continue
charging their current prices.
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Figure 13.6: Deriving the Reaction
Functions for Specific Duopolists
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Figure 13.7: The Stackelberg Leader’s
Demand and Marginal Revenue Curves
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Figure 13.8: The Stackelberg
Equilibrium
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Comparison Of Outcomes
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Figure 13.9: Comparing Equilibrium
Price and Quantity
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Competition When There Are Increasing
Returns To Scale
In markets for privately sold goods, buyers
are often too numerous to organize
themselves to act collectively.
Where it is impractical for buyers to organize
direct collective action, it may nonetheless be
possible for private agents to accomplish much
the same objective on their behalf.
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Figure 13.10: Sharing a Market with
Increasing Returns to Scale
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The Chamberlin Model
Assumption: a clearly defined “industry group,”
which consists of a large number of producers of
products that are close, but imperfect, substitutes
for one another.
Two implications:
1. Because the products are viewed as close substitutes,
each firm will confront a downward-sloping demand
schedule.
2. Each firm will act as if its own price and quantity
decisions have no effect on the behavior of other firms
in the industry.
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Figure 13.11: The Monopolistic
Competitor’s Two Demand Curves
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Figure 13.12: Short-Run Equilibrium
for the Chamberlinian Firm
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Figure 13.13: Long-Run Equilibrium
in the Chamberlin Model
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Perfect Competition Versus Chamberlinian
Monopolistic Competition
Competition meets the test of allocative efficiency, while
monopolistic competition does not.
Monopolistic competition is less efficient than perfect
competition because in the former case firms do not
produce at the minimum points of their long-run average
cost (LAC) curves.
In terms of long-run profitability the equilibrium positions
of both the perfect competitor and the Chamberlinian
monopolistic competitor are precisely the same.
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Figure 13.14: An Industry in Which
Location is the Important Differentiating
Feature
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The Optimal Number of Locations
The number of outlets that emerges from the
independent actions of profit-seeking firms will in
general be related to the optimal number of outlets
in the following simple way:
Any environmental change that leads to a change in the
optimal number of outlets (here, any change in
population density, transportation cost, or fixed cost)
will lead to a change in the same direction in the
equilibrium number of outlets.
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Figure 13.15: Distances with N Outlets
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Figure 13.16: The Optimal Number
of Outlets
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Figure 13.17: A Spatial Interpretation
of Airline Scheduling
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Why not have a flight leaving every 5
minutes, so that no one would be forced to
travel at an inconvenient time?
The larger an aircraft is, the lower its average
cost per seat is.
If people want frequent flights, airlines are forced to
use smaller planes and charge higher fares.
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Figure 13.18: Distributing the Cost
of Variety
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Figure 13.19: The Hot Dog Vendor
Location Problem
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Consumer Preferences And Advertising
Because products are differentiated,
producers can often shift their demand
curves outward significantly by advertising.
The revised sequence: the corporation
decides which products are cheapest and
most convenient to produce, and then uses
advertising and other promotional devices
to create demand for them.
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Figure 13.20: A Political
Location Problem
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